A person has a 1/3000 chance of having COVID-19. Find the probability that out of 6 people, at least one of them has COVID-19.
A person has a 1/3000 chance of having COVID-19. Find the probability that out of 6 people, at least one of them has COVID-19.
1 6
If 1 person has ——— probability, then with 6 persons there's ——— probability that one of them has it.
3,000 3,000
6/3000 reduces to 1/500 which, expressed as a decimal fraction, is 0.002 or expressed as a percent, is 0.2%.
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+2490 This is not the correct method to solve this type of problem. The solution method requires the use of the Binomial CDF. Your answer is (very close to) correct, but only because the probability and sample size are very small.
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Did you come here to criticize me, or to help the student who asked a question?
If it was the former, thanks for the input. If it was the latter, nice try but no cigar.
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+2490 Did you come here to criticize me, or to help the student who asked a question?
If it was the former, thanks for the input. If it was the latter, nice try but no cigar.
If I wanted to help the student, I would have (also) posted a solution. I chose not to because this question is presented (seemingly) by an indifferent, uninterested student. There are dozens of questions on this forum that use the Binomial CDF for a solution. This question is very basic: it’s a homework question assigned by a teacher. It is reasonable to assume the student attended a lecture and lesson prior to its assignment. So the student should be familiar with the term Binomial CDF and its application for this question –at least enough to research and learn the rote mechanics to present a solution.
You could research this, and present a solution to the student. I doubt the student will return to his question, but you will learn something and then can tutor next student who presents a similar quest. …And you can keep the cigar as a tip.
From this, it should be clear that I posted to criticize you. However you should note the criticism is in a constructive form, without the aggressive, ass-ripping commentary peppered with vulgarities usually reserved for the forum’s BB class (Blarney Bag, Bullshit Bug, Bubble Bain).
These BBs are the poster children old farts representing the indefatigable dumbshits united in errant math, and the personifications of stubborn, relentless, intractable bullshitters of mathematical lore. They are pseudo intellectuals who are all titled with a multiplicity of advanced dimwit degrees in arrogant stupidity. This forum does not lack for these professors of misinformation, who teach their absurdities with authority, irritation, and brain-dead dumbness. ... One reason for this excess is this forum allows for anonymous posting. Anonymous posting is one of several common denominators for all of the “BBs”.
You are anonymous and you are a (near) retirement-age male with an interest in mathematics, but with limited skills. I’m not yet sure to which category you belong. …Time will tell..., but I don’t believe you will become another BB. At least I hope not; we already have more than our fair share. 
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+118667 Believe it or not initial guest answerer, this is Ginger's way of saying that she likes you.
OR at least that she does not dislike you yet. LOL
Here is an answer that you can learn from.
The probability that 1 person has it is 1/3000
The prob that a person does not have it is 2999/3000
If there are 6 people in a room the prob that no one has it is (2999/3000)^6
so
the prob that at least 1 of the 6 people has it is 1- (2999/3000)^6 which is approx 0.002
